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# Sort sort small arrays eg 2 or 3 by explicit

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Unformatted text preview: hanges ! Simple Simple insertion faster for smaller arrays, a common optimization is to use it for subarray subarray with fewer than about 25 items ! For For sorted arrays, even bubble sort is faster faster than quicksort – Use Bsort for best “compromise” 25 Quicksort: Tail Recursion ! Any recursive function of the form: function (a, b, c) { ... function (x, y, z); } Can be rewritten as: function (a, b, c) { while (TRUE) { ... a = x; b = y; c = z; } } (some compilers do this automatically) 26 Quicksort: Quicksort: Tail Recursion qsort (r, lb, ub) { ... qsort qsort (r, lb, down - 1); qsort (r, down, ub); } becomes qsort (r, lb, ub) { while (TRUE) { ... qsort qsort (r, lb, down - 1); lb = down; // upper = upper } } 27 Quicksort: Tail Recursion ! Reduces Reduces required max stack size ! In In qsort(): perform the recursive call for the the smaller subarray first – Smaller subarray usually requires less stack Smaller space (fewer recursions) – With tail recursion and sorting the smaller With subarray first, the worst case is O(log n) (log because the smaller subarray is a most size n/2 and the larger subarray does not require a /2 function function call (it would use iteration) 28 An An Improved Quicksort Function Function qsort (r, lb, ub): qsort_tr(r, qsort_tr(r, lb, ub); insertion_sort(r, lb, ub); Function qsort_tr(r, lb, ub): while while ub – lb > smallsize pivot_idx = partition(r, lb, ub); if pivot_idx < (lb+ub)/2 qsort_tr(r, lb, pivot_idx-1); pivot_idxlb = pivot_idx+1; else qsort_tr(r, pivot_idx+1, ub); ub = pivot_idx-1 pivot_idx- 29 Quicksort: Summary ! Good pivots are necessary – Fortunately, we have O(n) time to choose it Fortunately, – Optimal pivot would split file evenly ! Median-of-three (Meansort) is usually of-three good good enough (and faster) ! Bad Bad quicksort implementation performs poor for (almost) sorted input and many equal equal keys (no good pivot exists) 30...
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